Computer aided engineering (CAE) has been used for supporting engineers in tasks such as analysis, simulation, design, manufacturing, etc. In a conventional mechanical engineering design procedure, CAE analysis (e.g., finite element method (FEM), boundary element method (BEM), finite difference analysis, meshless analysis, etc.) has been employed to evaluate structural responses (e.g., stresses, displacements, etc.).
With advent of the digital computer, many engineering simulations are more sophisticated, it requires coupling of more than one aforementioned method to accomplish. For example, FEM-BEM coupling can be used for simulating physical phenomena of electromagnetism, fluid-structure interaction, and others.
Coupling of these two numerical methods can sometimes be problematic especially involving a sliding boundary between two objects. For example, simulating operations of firing an electromagnetic rail-gun requires coupling of FEM-BEM with a sliding contact interface. Rail-gun comprises a pair of parallel rails and a projectile situated therebetween. When a large electrical current passes through the projectile between the pair of rails, a strong magnetic field force is generated to accelerate the projectile. In a numerical simulation using FEM-BEM, rails and projectile are represented with a FEM model (e.g., solid elements), while the electrical magnetic field in the surrounding air is represented by a BEM mesh. The BEM mesh is generated from the FEM model, as the outside surface of the FEM model.
Dealing with a sliding contact in BEM is complicated because the integrals defining the BEM matrices entries become singular for neighboring BEM faces, thereby it is necessary to avoid any hole in the BEM surface mesh. Many of the prior art approaches have been imposing constraints to “hanging” nodes along the contact boundary. However, the simulation results of these prior art approaches are generally poor. It is noted that “hanging” nodes are caused by relative movements between the projectile and the rails.
Therefore, it would be desirable to have methods and systems for handling sliding contact interface in a coupling procedure of finite element method (FEM) and boundary element method (BEM), such that simulations of fast moving object in an electromagnetic field can be conducted.